Nanook
Full House
I am also guessing you are using too much pressure. I have never had a chip break, much less break a ceramic chip. The idea is to slowly bend the warped chips back to the shape of the (Flat) ceramic chip, not force the ceramic chip into the warped shape of the clay chip. You clearly did the opposite... It takes a little heat and a little pressure and some time. Too much of one and lack of the others is not better, clearly it is worse....2+ hours
Those clamps you are using are probably not giving you good feedback on just how tight you are actually making them. With quick clamps you just need a little squeeze and then after about 15-20 minutes of cooling I give them another light squeeze then just let them cool for a total of about an hour or so. At the 1 hour mark they are cool to the touch and likely room temp all the way through. Nothing more is going to happen at this point. You won't do any harm by letting them sit longer, but they are not getting any flatter either.
If after your first attempt they are not flat then just run the entire set through again. I have had a few chips where I have had to run them through the process 3x, but that is pretty rare.